How to make a pure white smoke with blender internal render engine (not Cycles)
If you want to make smoke brighter, you need to make color of the smoke  brighter than white. This is howto:


In material settings make reflection color completely black:




As you can see, it doesn't affects at all, because this setting rewrites by smoke texture.  


Next, go to the texture settings and find reflection color. Put here something like 5.0. (To set value above the limits click on value and print the number from keyboard)




This setting mix value 5 times more different than original (black in material settings) color of smoke reflection.

Also, you can set "extra-white" color in smoke color setting: 

Select emiter of the smoke (not domain) and in phisics tab find smoke color setting